Question

A borrower took out a loan of 100,000 and promised to repay it with a payment at the end of each year for 30 years.

The amount of each of the first ten payments equals the amount of interest due. The amount of each of the next ten payments equals 150%% of the amount of interest due. The amount of each of the last ten payments is X.

The lender charges interest at an annual effective rate of 10%%.

Calculate X.

a.3,204

b.5,675

c.7,073

d.9,744

e.11,746

Answer 1

d. 9744

In order to amortize the loan,

The borrower decided to only pay the interest component for the first 10 years ,

Hence Payment = Interest

= 100,000 *.10 = 10,000

The principal component remains unaffected as the payment keeps on amorting the interest only.

Hence ,

Principal outstanding at the end of 10 years = 100,000.

Now the payment increased to 1.5* interest.

So Amount remaining

= 1.5*(p*0.1) * ( 1-(1+0.1)^-10) ÷0.1 = 59874

So,

Value of X

= P*i / 1-(1+i)^-t

Or

=59874*0.1. /. 1-(1+.1)^-10

=9744